http://iscoresports.com/

A player bunted for a hit and I scored it using "In Play" -> Bunt. When I looked at the stats for the game afterwards, the player was awarded a hit, but was given no singles (the column "1B" had a "0" in it). Instead the column "B" had a "1" in it. I am unfamiliar with a separate type of hit known as a "Bunt".

I agree, I think this is a little confusing, but you have it right. iScore breaks it down by B, 1B, 2B, 3B and HR. The totals of those are Total Hits. Bunt is basically a subcategory of single.

While it is statistically a single, many would like to know how many bunt singles a player may have.